1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. -a. Write down the firm's production possibility set, and its input requirement set.“b. Is this production function concave, quasi-concave?c. Is this production function homogenous, homothetic? +d. Find its returns to scale when x1=1, and x2=1.e

Firm's production function y=x11/2+x1 x2 where x1≥0 and x2≥0

Answered: Let y = f(x1, x2)=x112+x1X2 be a firm's…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L^1/2M^1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)
Use second image for reference, for part b here is referene; The maximum profit is found at the tangency between the production function and the isoprofit line. In other words, the slope of the production function and the slope of the isoprofit line must be the same. This is written as MPL = w where w is the slope of the isoprofit line. Then we get sqrt1 / 2L = w => 1/2w = sqrtL => L*D = 1/4w^2
Let a firm's production function be f(K, L) = min{2K, L}. a) Solve for the contingent demand functions for K and L.
24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.
Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? a) q=L+K b) q=LaKb c) q= L+ LaKb + K
For the production function Qs = K0.5L0.7 find the returns to scale, recall that a doubling of inputs that doulbes output is a CONSTANT returns to scale = 1.0
The production function for good X in the table below exhibits increasing marginal returns to capital over what outout range? Production Function for Good X Choose Multiple Choice: Between o and 1,524 Between 2,391 and 3,048 Between o and 2,991 Between 3,016 and 2,945 L* K MPK=(AQ/AK) AP=(Q/K) Marginal Product of Average Product of Capital Labor Capital Output Capital 10 57 5.7 5.70 20 324 26.7 16.20 30 657 33.3 40 1,072 41.5 26.80 se 1,524 45.2 30.48 6e 1,976 45.2 32.93 70 2,391 41.5 34.16 se 2,724 33.3 34.e5 9e 2,991 A 33.23 100 3,048 5.7 30.48 11e 3,016 -3.2 27.42 120 2,945 -7.1 24.54
A firm has the production function f(x, y) = x®y0.3, where a>0.7. This firm has Select one: a. decreasing returns to scale and increasing marginal product for factor x and y. b. None of the above. c. increasing returns to scale and diminishing marginal product of factor x. d. constant returns to scale. e. decreasing returns to scale and diminishing marginal products for factor y.
b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
Does the production function y=0.8x_1x_2 exhibit constant returns to scale, increasing returns to scale, decreasing returns to scale, or homothetic returns to scale
With a production function like Y=zN, which of the following must be true at the optimum? A).The marginal product of labor is smaller than real wage. B).The marginal product of labor is bigger than real wage. C).The representative firm makes positive profits. D). Profits of the representative firm are zero.

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